Complexity from Simplicity

This topic is in the very heart of my research. I am fascinated by the questions of how simple mechanics can create highly complex behaviors, structures, patterns and dynamics. This phenomenon of complexity-from-simplicity can be found everywhere,

  • from the way how the universe emerged, how matter itself arises,

  • how life emerged from non-living constituents,

  • how evolution creates diversity of the "tree of life",

  • how an embryo develops,

  • how physiological and immunological systems work,

  • how an ecosystem unfolds itself,

  • how swarm intelligence arises from a swarm of seemingly dump actors,

  • how a thought might appear in someone's brain,

  • how such a thought can then spread and develop into a society,

  • even shaping or creating society itself by further developing and diversifying it,

  • producing a memetic process in analogy to an evolutionary genetic process.

Complexity is all around us, everywhere, at all time, and it appears on all time scales and on all size scales. Complexity appears in layers of even more complexity and the deeper you dig in the networks of cause and effect, the more surprises you may find. Until, in very rare moments, you may reach suddenly a layer where you find an unexpected level of simplicity and say "WTF? How? Why?" These are the moments I am always seeking for: The moments of fundamental understanding, when seemingly complex phenomena can ultimately be explained by a set of simple mechanics. However, such moments always hold just for their moments, because as soon as one looks deeper ... even more complexity usually appears.

Mathematical modeling, computer simulation, in combination with empirical experimentation are the key methodologies I use. Most prominently I target questions around swarm intelligence (e.g. in honeybees) or artificial swarm systems (robot swarms, reconfigurable multi-modular robotics) with theoretical and with empirical research methods in parallel. Besides that, topics like pattern formation, swarm algorithms, evolutionary mechanisms and ecological dynamics are in my research interest mainly with theoretical studies, so far.

The Primordial Particle System

This is a very simple computer model of a set of particles that interact with each other in a very simple way: Each of these self-propelled particle's orientation is affected by the number of neighbors on either side of the particle within a given radius. And this is the only rule! This simple interaction behavior, which is in fact much simpler than the rules that govern a bird flock or a fisch shoal, leads to the emergence of fascinating dynamic structures that exhibit high complexity. The habitat gets occupied by cells and spores that spread out and "conquer their world", interact with each other and then a full blown "ecosystem" of these structures unfolds, with close macroscopic resemblance to known dynamics of our natural ecosystems. All of this is emerging from one very simple motion law of particles. To my knowledge, this is the simplest form of such a life-like system, even simpler than the famous Game of Life (by John Conway), which requires three rules, perfect synchrony of agents and a noise-free environment. A PPS does not require these prerequisites, it even works "better" under imperfect conditions.

See Schmickl, T., Stefanec, M., & Crailsheim, K. (2016). How a life-like system emerges from a simplistic particle motion law. Scientific Reports (Nature Publisher Group), 6, 37969 for more information (Open Access).

A screenshot of the PPS system (many blue, green, yellow and magenta) particles that form shapes that resemble "cells" or "spores" in this self-propelled particle system

A Screenshot of the Primordial Particle System in action.

an artistic drawing showing wasps that collect water and pulp and build their nest combs from these materials

Artistic drawing summarizing the components of the common stomach system. (by courtesy of Asya Ilgun)

The Common Stomach Model

One important aspect of social insects is their system of organizing their work within the colony in a decentralized and self-organized way. Key features are characterized by dynamically regulated division of labor, which is the choosing of a task amongst a set of available tasks, and by adaptively allocated task partitioning, which is the splitting up of a task into sub-tasks. In my research I created many mathematical models in order to investigate such features in ants, in honeybees and in paper wasp colonies. From these findings I derived the functional core of the system and modeled it in a set of simple mathematical equations. This level of abstraction allowed then to translate these mechanisms into other contexts, like robot swarms or swarm intelligent algorithms. In establishing a novel bio-inspired technology, I always follow a set of strict principles and a very specific research methodology:

Step 1: Observing the natural source of inspiration,

Step 2: Extracting the core mechanisms from these observations,

Step 3: Expressing these core mechanics in abstract mathematical formulation,

Step 4: Re-implementing these mechanics in novel algorithmic implementations,

Step 5: Finally, re-embodiment of these systems on different size and time scales in the form of technological artifacts, e.g. robot swarms.
(read more)

The BEECLUST Algorithm

The BEECLUST algorithm is based on observing the natural group behavior of honeybees. It is a swarm-intelligent algorithm which we think is the most simple swarm algorithm that can still create a smart swarm. Such swarms can choose between multiple optimal spots, picking out the optimal one. The quality of a spot can be derived from multiple physical factors. Tests have been made with light gradients, temperature gradient fields, magnetic fields, electrical fields and water depth as a local environmental cue. (read more)

a group of bees aggregating around a warm (heating) coil

Bees aggregate in favorable spots based on the individual actions that they coordinate in the group

A flase-color (IR picture like) heatmap of an arena showing 2 clusters of bees aggregating in warmer spots.

The individual behavior and the merging swarm behavior was explored in choice experiments thoroughly

several epuck robots with colored LEDs

These behaviors have then been translated into robot algorithms, enabling also these swarms to make swarm-intelligent decisions